Another important aspect for the progress of QEC is to inform the theoretical descriptions, which typically assess a particular QECC under a specific noise model, with experimental results such that the noise model can be made as realistic as possible. In the context of trapped ions, a recent effort along these lines has been accomplished for the shuttling-based approach [1]}, [2]}, [3]}, [4]} as well as for the single-string approach [5]}, [6]}, [7]}. In this manuscript, motivated by the recent developments of new addressing optics [8]}, [9]}, which allow addressing subsets of ions in strings, we focus on the single-string approach. Specifically, we present a microscopically-motivated error model that accounts for imperfections in all the required operations. A particular focus is placed on crosstalk errors. As described in [10]}, crosstalk errors cause undesired dynamics that violate either
(or both) of two principles: spatial locality (i.e. gates should only affect the target qubits) and independence of local operations (i.e. the effect of a gate should be independent of other gates being applied to the system). In ion traps, crosstalk is caused by residual illumination of laser light on neighbouring ions when applying single- and two-qubit gates. This error source can be effectively minimised for single-qubit gates [11]} using composite pulse sequences and dynamical decoupling techniques [12]} but becomes a more delicate issue when arising in the context of two-qubit entangling gates.
With the use of carefully constructed pulse sequences, it is possible to suppress unwanted couplings on multi-qubit coupling operations, as shown in [13]}, [14]}.
In this work, we consider two different models of crosstalk errors caused by this residual illumination. In the context of fault-tolerant quantum computation (FTQC), fault-tolerant constructions assume that errors only happen on those qubits that are involved in the gates. Thus, crosstalk represents an error source that potentially breaks the fault-tolerant character of FT circuit constructions, as it can induce error processes affecting groups of physical qubits that would, otherwise, not interact through the gates. In this way, the FT design of the circuits is compromised, possibly leading to the proliferation of errors. Therefore, if crosstalk is not adequately accounted for, or suppressed, it can have a damaging effect on the performance of the QEC protocol and break fault tolerance [15]}, [16]}, [17]}, [18]}, [19]}, [20]}.
